\sect{Fermions in a gravitational field}

%Baruch's  B12.

Consider fermions of mass $\mass$ and spin $1/2$ in a gravitational field
with constant acceleration $g$ and at uniform temperature $T$. 
The density of the Fermions at zero height is $n(0)=n_{0}$.
In item (3) assume that at zero height the fermions form a degenerate 
gas with Fermi energy $\epsilon_{F}^{0}$ that is much larger compared with~$T$. 

\begin{enumerate}

\item Assume that the fermions behave as classical particles and
find their density $n(h)$ as function of the height.

\item Assume $T=0$. Find the local Fermi momentum $p_{F}(h)$ 
and the density $n(h)$  as function of the height.

\item Assume low temperatures. Estimate the height $h_{c}$ such that 
for $h\gg h_{c}$ the fermions are non-degenerate. 

\item In the latter case find $n(h)$ for $h\gg h_{c}$, given as before $n_0$ at zero height.

\end{enumerate}

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